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    "# Thrust Vectoring Analysis\n",
    "\n",
    "Based on a NASA report - [Optimal Pitch Thrust-Vector Angle and Benefits for all Flight Regimes](https://ntrs.nasa.gov/api/citations/20000034897/downloads/20000034897.pdf)\n",
    "\n",
    "Use JSBSim to compare how varying the thrust vector angle can minimize fuel\n",
    "burn for a given flight condition and compare the results to the NASA report.\n",
    "\n",
    "Tests performed for a cruise condition and for a climb condition."
   ]
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   "source": [
    "# Confirm that JSBSim is installed. If not and running on Google Colab\n",
    "# then install JSBSim into the Google Colab instance.\n",
    "\n",
    "import os\n",
    "\n",
    "try:\n",
    "  import jsbsim\n",
    "  print('JSBSim is installed')\n",
    "  # Relative path to the directory where the flight model is stored\n",
    "  # Note - Aircraft directory needs to be writeable in order to modify the cg\n",
    "  PATH_TO_JSBSIM_FILES=\"../..\"\n",
    "  print(f'Current working directory: {os.getcwd()}')\n",
    "except ImportError:\n",
    "  import sys\n",
    "  if 'google.colab' in sys.modules:\n",
    "      print('Installing JSBSim...')\n",
    "      !pip install jsbsim\n",
    "      # Use the standard aircraft supplied by the JSBSim Python package\n",
    "      PATH_TO_JSBSIM_FILES=None"
   ]
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    "import jsbsim\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# --- Configuration Section ---\n",
    "# Global variables that must be modified to match your particular need\n",
    "# The aircraft name\n",
    "# Note - It should match the exact spelling of the model file\n",
    "AIRCRAFT_NAME=\"737\"\n",
    "\n",
    "# --- JSBSim Initialization ---\n",
    "# These lines initialize the flight dynamics model.\n",
    "\n",
    "# Avoid flooding the console with log messages\n",
    "jsbsim.FGJSBBase().debug_lvl = 0\n",
    "\n",
    "# Create a flight dynamics model (FDM) instance.\n",
    "fdm = jsbsim.FGFDMExec(PATH_TO_JSBSIM_FILES)\n",
    "\n",
    "# Load the aircraft model\n",
    "fdm.load_model(AIRCRAFT_NAME)\n",
    "\n",
    "# Set engines running\n",
    "fdm['propulsion/set-running'] = -1\n",
    "\n",
    "\n",
    "def thrust_vector_range_test(altitude, speed, flight_path_angle, title):\n",
    "    # altitude: altitude above sea level (ft)\n",
    "    # speed: mach number of speed (<1)\n",
    "    #        calibrated airspeed (kts) (>=1)\n",
    "    # flight_path_angle: flight path angle (deg)\n",
    "    # title: title for plot\n",
    "\n",
    "    # Thrust vectoring angles in pitch (deg) to test\n",
    "    tv_angles = np.linspace(0, 10, 100)\n",
    "\n",
    "    # Thrust and AoA trim results storage\n",
    "    thrusts = []\n",
    "    alphas = []\n",
    "\n",
    "    # Initialize the minimum thrust and thrust vectoring angles to a very large number\n",
    "    # to track/record the minimum thrust and the angle at which the minimum occurs.\n",
    "    min_thrust = 1000000  # thrust (lbf)\n",
    "    min_angle = 100       # Thrust Vector Angle in pitch (deg)\n",
    "\n",
    "    # Iterate each thrust vector angles in pitch.\n",
    "    for tv_angle in tv_angles:\n",
    "\n",
    "        # --- Simulation Initialization ---\n",
    "        # This line initializes the flight dynamics model.\n",
    "\n",
    "        # Initial conditions\n",
    "        fdm['ic/h-sl-ft'] = altitude  # altitude above sea level (ft)\n",
    "        # Check the speed and set the value according to if the speed is mach or kts\n",
    "        if speed < 1.0:\n",
    "            fdm['ic/mach'] = speed  # mach number of speed\n",
    "        else:\n",
    "            fdm['ic/vc-kts'] = speed # calibrated airspeed (kts)\n",
    "        fdm['ic/gamma-deg'] = flight_path_angle  # flight path angle (deg)\n",
    "\n",
    "        # Initialize the aircraft with initial conditions\n",
    "        fdm.run_ic()\n",
    "\n",
    "\n",
    "        # --- Simulation running ---\n",
    "        # These lines run the simulation.\n",
    "\n",
    "        # Trim the aircraft.\n",
    "        try:\n",
    "            # Set thrust vector angle in pitch (deg) for both engines\n",
    "            fdm[\"propulsion/engine[0]/pitch-angle-rad\"] = math.radians(tv_angle)\n",
    "            fdm[\"propulsion/engine[1]/pitch-angle-rad\"] = math.radians(tv_angle)\n",
    "\n",
    "            # Trim the aircraft.\n",
    "            # 1 means straight flight by using all changeable control variables.\n",
    "            fdm['simulation/do_simple_trim'] = 1\n",
    "\n",
    "            # Record the simulation data.\n",
    "            # Append the angle of attack to the result storage.\n",
    "            alphas.append(fdm[\"aero/alpha-deg\"])\n",
    "            # Append the thrust to the result storage.\n",
    "            thrust = fdm[\"propulsion/engine[0]/thrust-lbs\"]*2  # because there are two engines\n",
    "            thrusts.append(thrust)\n",
    "\n",
    "            # Update the minimum thrust and thrust vectoring angles.\n",
    "            if thrust < min_thrust:\n",
    "                min_thrust = thrust\n",
    "                min_angle = tv_angle\n",
    "\n",
    "        except jsbsim.TrimFailureError:\n",
    "            print(\"Trim failed....\")\n",
    "            pass  # Ignore trim failure\n",
    "\n",
    "\n",
    "    # --- Plot Results ---\n",
    "    # This section plots the simulation results.\n",
    "\n",
    "    plt.rcParams[\"figure.figsize\"] = (12, 8)  # Set the figure size for matplotlib plots.\n",
    "    fig, ax1 = plt.subplots()\n",
    "    plt.title(title)\n",
    "\n",
    "    # Plot the thrust values against the thrust vector angles.\n",
    "    ax1.plot(tv_angles, thrusts, label='Thrust')\n",
    "    # Plot the minimum thrust as a red scatter point.\n",
    "    ax1.scatter(min_angle, min_thrust, color='red', label=f'Minimum Thrust at {min_angle:.2f} deg')\n",
    "    ax1.set_xlabel('Thrust Vector Angle (deg)')\n",
    "    ax1.set_ylabel('Thrust (lbf)')\n",
    "\n",
    "    # Create the second y-axis for AoA\n",
    "    ax2 = ax1.twinx()\n",
    "    ax2.set_ylabel('Alpha (deg)')\n",
    "    # Plot the alpha values against the thrust vector angles.\n",
    "    ax2.plot(tv_angles, alphas, color='green', label='Alpha')\n",
    "\n",
    "    ax1.legend(loc='upper center')\n",
    "    ax2.legend(loc='center right')\n",
    "\n",
    "    # Save the figure as an SVG file.\n",
    "    plt.savefig(f\"{title}.svg\", format=\"svg\")\n",
    "\n",
    "    # Show the plot.\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "# Cruise conditions - 30,000ft Mach 0.8\n",
    "thrust_vector_range_test(30000, 0.8, 0, 'Cruise - 30,000ft Mach 0.8')\n",
    "\n",
    "# Climb conditions - 15,000ft 300KIAS flight path angle of 3 degrees\n",
    "thrust_vector_range_test(15000, 300, 3, 'Climb - 15,000ft 300KIAS FPA 3 deg')"
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